Star Trek is a franchise where a starship that uses natural crystals to fly thousands of times faster than the speed of light visits planets where aliens routinely speak English and look pretty human. Science went out the door with Star Trek about 57 years ago.
He used a Subspace Field to do that, which is just another name for the Warp Field used by starships.
Really, the whole Dilithium storyline in Discovery was just bad writing. There are a thousand and one different ways to generate power. And a thousand and one different ways to transfer that power around. Meaning that while whatever you end up with might not have the efficiency of M/AM reactors. It's not a particularly difficult problem for anyone with two brain-cells to rub together to overcome.
Dilithium is NOT used to generate power. It's crystalline matrices is one (of the very few) things that can properly and safely mix matter and anti-matter so that it (m-a/m) can power the drive.